Darren Edwards’ men headed into Friday’s fixture with just one win in four RaboDirect PRO12 games but they were good value for this convincing victory.
Tom Riley crossed for the game’s only try after 24 minutes, while man of the match Jason Tovey kicked five penalties and a conversion.
Outside centre Riley made the most of a hole in the Ulster midfield after opposite number Nevin Spence had seen yellow for a high tackle on Dragons debutant Tonderai Chavhanga just a minute earlier. Riley saw off Luke Marshall on his way to the line as the home side moved 11-3 in front.
Tovey added the conversion to his eighth and 19th-minute penalties before slotting two more before the break, with Paddy Jackson’s two penalties Ulster’s only first-half scores.
The second period saw the sides share just a further six points, with Tovey’s fifth penalty arriving seven minutes in and Jackson’s third coming four minutes later.
The Northern Irish province looked to have thrown themselves a lifeline with 12 minutes remaining when Ian Whitten headed for the corner but Tovey’s last-gasp tackle saved a certain try.
Victory sees the Dragons climb above the Scarlets, Treviso and Glasgow ahead of the rest of this weekend’s fixtures.
